Probability of a Straight Flush
Date: 5/15/96 at 14:44:22 From: Art Mabbott Subject: Probability Problem My high school math topics class is trying to work through a probability problem involving counting and trees. The question involves finding the probability of drawing 5 spades, that is P(a flush) = (13 12 11 10 9)/(52 51 50 49 48) P(flush of any suit) = 4 P(a flush) The question is, what is the P(Straight flush) = ? (knowing that there are only 10 ways in each suit to draw a straight flush). Art Mabbott
Date: 5/17/96 at 19:0:51 From: Doctor Ken Subject: Re: Probability Problem Hello! Something that will help in these problems is the "choose" formula. If you want to know the number of ways you can choose 5 cards from a deck of 52 cards, when the order of the cards doesn't matter, then the answer is 52 choose 5, which is 52!/(5!(52-5)!) = (52 51 50 49 48)/(5 4 3 2 1). So that's the total number of different hands you could be dealt. Since you've already figured out how many different ways you can get a straight flush (actually, are you sure it's 10 in each suit? I get 9, because A2345 doesn't count, right?), you can just divide the number of straight flushes by the number of possible hands to get the probability you're dealt a straight flush. -Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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